Quadrature mismatch shaping with a complex, data directed swapper

Quadrature bandpass (QBP) Sigma Delta ADCs require a feedback path for both the I and the Q part of the complex feedback signal. A complex DAC could give this feedback with near-perfect I/Q balance. Still, the mismatch between the unit elements of the complex DAC introduces mismatch noise that should be shaped out of the signal band with dynamic element-matching (DEM) techniques. To select the unit DAC elements of the complex multibit DAC, the well-known data directed swapper is generalized towards a complex structure and the necessary constraints for its correct functioning are derived. Additionally, a hardware efficient structure is presented: the reduced butterfly shuffler. Here, some of the QBP swapper cells are replaced by bandpass (BP) swapper cells. Also, great attention is paid to the interconnection pattern of the data directed swapper to prevent instability